SVD-NO: Learning PDE Solution Operators with SVD Integral...

Authors

Noam Koren Computer Science Department, Technion-Israel Institute of Technology, Haifa, Israel
Ralf J. J. Mackenbach EPFL - EPF Lausanne
Ruud J. G. van Sloun Eindhoven University of Technology
Kira Radinsky Computer Science Department, Technion-Israel Institute of Technology, Haifa, Israel
Daniel Freedman Department of Applied Mathematics, Tel Aviv University, Tel Aviv, Israel

DOI:

https://doi.org/10.1609/aaai.v40i1.37016

Abstract

Neural operators have emerged as a promising paradigm for learning solution operators of partial differential equations (PDEs) directly from data. Existing methods, such as those based on Fourier or graph techniques, make strong assumptions about the structure of the kernel integral operator, assumptions which may limit expressivity. We present SVD-NO, a neural operator that explicitly parameterizes the kernel by its singular-value decomposition (SVD) and then carries out the integral directly in the low-rank basis. Two lightweight networks learn the left and right singular functions, a diagonal parameter matrix learns the singular values, and a Gram-matrix regularizer enforces orthonormality. As SVD-NO approximates the full kernel, it obtains a high degree of expressivity. Furthermore, due to its low-rank structure the computational complexity of applying the operator remains reasonable, leading to a practical system. In extensive evaluations on five diverse benchmark equations, SVD-NO achieves a new state of the art. In particular, SVD-NO provides greater performance gains on PDEs whose solutions are highly spatially variable.

How to Cite

Koren, N., Mackenbach, R. J. J., van Sloun, R. J. G., Radinsky, K., & Freedman, D. (2026). SVD-NO: Learning PDE Solution Operators with SVD Integral Kernels. Proceedings of the AAAI Conference on Artificial Intelligence, 40(1), 525–533. https://doi.org/10.1609/aaai.v40i1.37016

Issue

Section

AAAI Technical Track on Application Domains I